91Ó°ÊÓ

Use the half-angle identities to find the exact values of the trigonometric expressions. $$\cot \left(\frac{13 \pi}{8}\right)$$

Solve the trigonometric equations exactly on the indicated interval, \(0 \leq x<2 \pi\). $$\sin x=-\cos x$$

Evaluate each expression exactly, if possible. If not possible, state why. $$\cot ^{-1}\left[\cot \left(\frac{5 \pi}{4}\right)\right]$$

Graph each of the functions by first rewriting it as a sine, cosine, or tangent of a difference or sum. $$y=\frac{1-\tan x}{1+\tan x}$$

Verify each of the trigonometric identities. $$\frac{\sin x+1-\cos ^{2} x}{\cos ^{2} x}=\frac{\sin x}{1-\sin x}$$

Use the half-angle identities to find the exact values of the trigonometric expressions. $$\cot \left(\frac{7 \pi}{8}\right)$$

Refer to the following: Sum and difference identities can be used to simplify more complicated expressions. For instance, the sine and cosine function can be represented by infinite polynomials called power series. $$ \begin{aligned} \cos x &=1-\frac{x^{2}}{2 !}+\frac{x^{4}}{4 !}-\frac{x^{6}}{6 !}+\frac{x^{8}}{8 !}-\cdots \\ \sin x &=x-\frac{x^{3}}{3 !}+\frac{x^{5}}{5 !}-\frac{x^{7}}{7 !}+\frac{x^{9}}{9 !}-\cdots \end{aligned} $$ Power Series. Find the power series that represents \(\cos \left(x-\frac{\pi}{4}\right)\)

Solve the trigonometric equations exactly on the indicated interval, \(0 \leq x<2 \pi\). $$\sec x+\cos x=-2$$

Verify each of the trigonometric identities. $$\sec x(\tan x+\cot x)=\frac{\csc x}{\cos ^{2} x}$$

Evaluate each expression exactly, if possible. If not possible, state why. $$\sec ^{-1}\left[\sec \left(-\frac{\pi}{3}\right)\right]$$